Question

E-Cigs According to the Centers for Disease Control and Prevention, 2.8% of high school students currently use electronic cigarettes. A high school counselor is concerned the use of e-cigs at her school is higher.

(a) Determine the null and alternative hypotheses.

(b) If the sample data indicate that the null hypothesis should not be rejected, state the conclusion of the school counselor.

(c) Suppose, in fact, that the proportion of students at the counselor’s high school who use electronic cigarettes is 0.034. Was a Type I or Type II error committed?

Answer 1

(a) H0:Null Hypothesis: P 0.028

HA; Alternative Hypothesis: P > 0.028

(b) Test result: Fail to reject null hypothesis. The difference is not significant.

Conclusion:
The data do not support the claim that the use of e-cigs at her school is higher.

(c) Type I Error: Rejection of a true null hypothesis.

   Type II Error: Filing to reject a false null hypothesis.

Here:

In reality, P = 0.034 which is greater than 0028. This shows that the null hypothesis is false. Thus, we are Failing to reject a false null hypothesis.

Thus

Type II error is committed.